{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Truncated stick breaking in greta\n", "\n", "Here, we briefly discuss truncated stick breaking (TSB). We use TSB as a finite-dimensional alternative to an infinite dimensional prior over the number of mixture components in a mixture model. We do the analysis in greta. TSB allows us to use continuous parameters entirely, which in turn allows us to use Hamiltonian Monte Carlo (and since most probabilistic programming languages do not allow discrete paramters). Also, in practice, working with continuous parameters is way easier than discrete ones (as with the Chinese restaurant process).\n", "\n", "We first try to use TSB with a mixture of univariate normals, and then with Poisson variables." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "suppressMessages(library(\"greta\"))\n", "suppressMessages(library(\"tensorflow\"))" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "suppressMessages(library(\"tidyverse\"))\n", "suppressMessages(library(\"MASS\"))\n", "suppressMessages(library(\"bayesplot\"))\n", "suppressMessages(library(\"caret\"))\n", "options(repr.plot.width=8, repr.plot.height=3)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "options(repr.plot.width=8, repr.plot.height=3)\n", "set.seed(23)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Normal data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We first create some data. We create a data set of $1000$ observations per mixture component." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "N <- 1000\n", "K <- 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We set the means of the mixture components to $\\boldsymbol \\mu = \\{ -2, 0, 2\\}$. We use a single standard deviations $\\sigma=0.25$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "mus <- c(-2, 0, 2)\n", "sd <- .25" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we create latent indicator variables $Z$ and sample normal data w.r.t to the cluster indicator." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "data <- vector(length = N * K)\n", "Z <- factor(rep(seq(K), each=N))\n", "for (k in seq(K)) { \n", " idx <- seq(N) + ((k - 1) * N)\n", " data[idx] <- rnorm(N, mus[k], sd)\n", "}" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAIAAAAXZAVmAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nQIAGAAAAVCBAAwAAACr8P5YdSzi3HYfdAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data.frame(data=data, idx=as.factor(rep(seq(K), each=N))) %>%\n", " ggplot(aes(data, fill=idx)) +\n", " geom_histogram(bins=30, position = \"dodge\") +\n", " scale_fill_viridis_d(\"Component\", alpha = 1, begin=.3, end=.8) + \n", " theme_minimal()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For our data set it should be fairly easy to find the correct number of clusters ($3$). For the TSB, we need to set the number of clusters to a sufficiently high $K$, to achieve a negligibly small error in comparison to a \"true\" infinite dimensional prior.\n", "\n", "See for instance https://projecteuclid.org/euclid.bj/1551862850 for a theoretical and practical justification for the truncation." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "K <- 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will only try to estimate the vector of mean values of the Gaussians. In order to avoid non-identifiability, we can use a small trick: we create a prior of means of length $K$ and, use the cumulative sum (cumsum), and ensure that the mean values are sorted and increasing in value. For instance:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\t
1. 0.593454854562879
2. \n", "\t
3. 0.856230824021623
4. \n", "\t
5. 1.22660479671322
6. \n", "\t
7. 2.02785729477182
8. \n", "\t
9. 2.67813442042097
10. \n", "\t
11. 3.13572235242464
12. \n", "
\n" ], "text/latex": [ "\\begin{enumerate*}\n", "\\item 0.593454854562879\n", "\\item 0.856230824021623\n", "\\item 1.22660479671322\n", "\\item 2.02785729477182\n", "\\item 2.67813442042097\n", "\\item 3.13572235242464\n", "\\end{enumerate*}\n" ], "text/markdown": [ "1. 0.593454854562879\n", "2. 0.856230824021623\n", "3. 1.22660479671322\n", "4. 2.02785729477182\n", "5. 2.67813442042097\n", "6. 3.13572235242464\n", "\n", "\n" ], "text/plain": [ "[1] 0.5934549 0.8562308 1.2266048 2.0278573 2.6781344 3.1357224" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x <- c(runif(1, -1, 1), runif(5, 0, 1))\n", "cumsum(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In greta that is:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "prior_mu_ordered <- cumsum(\n", " c(greta::variable(lower = -5, upper = 5),\n", " greta::variable(lower = 0, upper = 5, dim = K - 1)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we set a prior over the mixing weights. For this, as mentioned before, we use stick breaking. Luckily LaplacesDemon has a function for the sticks." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "stick_breaking <- function(theta) {\n", " LaplacesDemon::Stick(theta)\n", "}\n", "\n", "# note the K - 1 which is required for LaplacesDemon::Stick (yes it's dumb)\n", "prior_stick <- greta::beta(1, 1, dim = K - 1)\n", "prior_weights <- stick_breaking(prior_stick)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we set the mixture distribution and sample from the posterior. This is a little annoying in R, cause we need to do it manually." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "greta::distribution(data) <- greta::mixture(\n", " greta::normal(prior_mu_ordered[1], .25), \n", " greta::normal(prior_mu_ordered[2], .25),\n", " greta::normal(prior_mu_ordered[3], .25),\n", " greta::normal(prior_mu_ordered[4], .25),\n", " greta::normal(prior_mu_ordered[5], .25),\n", " greta::normal(prior_mu_ordered[6], .25),\n", " greta::normal(prior_mu_ordered[7], .25),\n", " greta::normal(prior_mu_ordered[8], .25),\n", " greta::normal(prior_mu_ordered[9], .25),\n", " greta::normal(prior_mu_ordered[10], .25),\n", " weights = prior_weights\n", ")" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "mod <- greta::model(prior_stick, prior_weights, prior_mu_ordered)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " warmup ====================================== 1000/1000 | eta: 0s \n", " sampling ====================================== 1000/1000 | eta: 0s \n" ] } ], "source": [ "samples <- greta::mcmc(mod, n_cores = 1, chains = 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see if we could identify the components." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "stat_bin() using bins = 30. Pick better value with binwidth.\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAIAAAAXZAVmAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bayesplot::mcmc_hist(samples, regex_pars = \"weights\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks like it suffices to use three components (as only three components of the weight posterior significant weight). Now, let's see if we could identify the means correctly. Since we only use components , we only consider these means." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAIAAAAXZAVmAAAABmJLR0QA/wD/AP+gvaeTAAAg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\nwoLzAAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bayesplot::mcmc_intervals(samples, regex_pars = \"mu\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That worked great. We were perfectly able to recover the correct number of components. Now, let's cluster them. We only cluster with the componentes 2, 3 and 4, since our posterior weights suggest, these are the important ones." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "posterior_matrix <- as.matrix(samples)\n", "posterior_mus <- posterior_matrix[,sprintf(\"prior_mu_ordered[%i,1]\", c(2, 3, 4))]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we assign each point its most likely assignment" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "clusters <- vector(length = length(data))\n", "for (i in seq(data)) {\n", " probs <- apply(posterior_mus, 2, function(.) mean(dnorm(data[i], ., .25)))\n", " clusters[i] <- which.max(probs) \n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we compute a confusion matrix to check our predictions." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Confusion Matrix and Statistics\n", "\n", " Reference\n", "Prediction 1 2 3\n", " 1 1000 0 0\n", " 2 0 1000 0\n", " 3 0 0 1000\n", "\n", "Overall Statistics\n", " \n", " Accuracy : 1 \n", " 95% CI : (0.9988, 1)\n", " No Information Rate : 0.3333 \n", " P-Value [Acc > NIR] : < 2.2e-16 \n", " \n", " Kappa : 1 \n", " \n", " Mcnemar's Test P-Value : NA \n", "\n", "Statistics by Class:\n", "\n", " Class: 1 Class: 2 Class: 3\n", "Sensitivity 1.0000 1.0000 1.0000\n", "Specificity 1.0000 1.0000 1.0000\n", "Pos Pred Value 1.0000 1.0000 1.0000\n", "Neg Pred Value 1.0000 1.0000 1.0000\n", "Prevalence 0.3333 0.3333 0.3333\n", "Detection Rate 0.3333 0.3333 0.3333\n", "Detection Prevalence 0.3333 0.3333 0.3333\n", "Balanced Accuracy 1.0000 1.0000 1.0000" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "caret::confusionMatrix(factor(clusters), Z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Poisson data \n", "\n", "Next we try a Poisson mixture." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "N <- 1000\n", "K <- 3\n", "mus <- exp(c(0, 1, 2))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "data <- vector(length = N * K)\n", "Z <- factor(rep(seq(K), each=N))\n", "for (k in seq(K)) { \n", " idx <- seq(N) + ((k - 1) * N)\n", " data[idx] <- rpois(N, mus[k])\n", "}" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAIAAAAXZAVmAAAABmJLR0QA/wD/AP+gvaeTAAAg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\n0IEADQAAAOjw/7X6EvbpIof4AAAAAElFTkSuQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data.frame(data=data, idx=as.factor(rep(seq(K), each=N))) %>%\n", " ggplot(aes(data, fill=idx)) +\n", " geom_histogram(bins=30, position = \"dodge\") +\n", " scale_fill_viridis_d(\"Component\", alpha = 1, begin=.3, end=.8) + \n", " theme_minimal()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We truncate the DP at $K=10$ as before and define the model." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "K <- 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use the same the trick from before. Since we exponentiate the means later, we don't need to care about negative values." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "prior_mu_ordered <- cumsum(\n", " c(greta::variable(lower = -5, upper = 3),\n", " greta::variable(lower = 0, upper = 3, dim = K - 1)))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "greta::distribution(data) <- greta::mixture(\n", " greta::poisson(exp(prior_mu_ordered[1])),\n", " greta::poisson(exp(prior_mu_ordered[2])),\n", " greta::poisson(exp(prior_mu_ordered[3])),\n", " greta::poisson(exp(prior_mu_ordered[4])),\n", " greta::poisson(exp(prior_mu_ordered[5])),\n", " greta::poisson(exp(prior_mu_ordered[6])),\n", " greta::poisson(exp(prior_mu_ordered[7])),\n", " greta::poisson(exp(prior_mu_ordered[8])),\n", " greta::poisson(exp(prior_mu_ordered[9])),\n", " greta::poisson(exp(prior_mu_ordered[10])),\n", " weights = prior_weights\n", ")" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "mod <- greta::model(prior_stick, prior_weights, prior_mu_ordered)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ " warmup ====================================== 1000/1000 | eta: 0s \n", " sampling ====================================== 1000/1000 | eta: 0s \n" ] } ], "source": [ "samples <- greta::mcmc(mod, chains = 1, n_cores = 1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How many components do we need?" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "stat_bin() using bins = 30. Pick better value with binwidth.\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAIAAAAXZAVmAAAABmJLR0QA/wD/AP+gvaeTAAAg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", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bayesplot::mcmc_hist(samples, regex_pars = \"weights\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, it's not so clear anymore. It looks as if we should use four components (so one too many), but this could be due to poor prior choice. What about the means?" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA8AAAAFoCAIAAAAXZAVmAAAABmJLR0QA/wD/AP+gvaeTAAAg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", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bayesplot::mcmc_intervals(samples, regex_pars = \"mu\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, let's have a look at the posterior assignments of the data points to the components again. In order to keep the cluster assignments (2, 3, 4, 5) the same as in our original assignment, we pick the second component last. By that when we call which.max it will return the correct indexes for the cluster, i.e. assignment to cluster 3 will be index 1 which corresponds to the cluster in our original assignment. Since we have four clusters to consider, the new cluster (component 2) will get index 4." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "posterior_matrix <- as.matrix(samples)\n", "posterior_mus <- posterior_matrix[,sprintf(\"prior_mu_ordered[%i,1]\", c(3, 4, 5, 2))]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "clusters <- vector(length = length(data))\n", "for (i in seq(data)) {\n", " probs <- apply(posterior_mus, 2, function(.) mean(dpois(data[i], exp(.))))\n", " clusters[i] <- which.max(probs) \n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since we have four clusters to consider now, we need to relevel our true latent assigments." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Confusion Matrix and Statistics\n", "\n", " Reference\n", "Prediction 1 2 3 4\n", " 1 375 175 9 0\n", " 2 241 625 122 0\n", " 3 3 149 869 0\n", " 4 381 51 0 0\n", "\n", "Overall Statistics\n", " \n", " Accuracy : 0.623 \n", " 95% CI : (0.6054, 0.6404)\n", " No Information Rate : 0.3333 \n", " P-Value [Acc > NIR] : < 2.2e-16 \n", " \n", " Kappa : 0.4725 \n", " \n", " Mcnemar's Test P-Value : NA \n", "\n", "Statistics by Class:\n", "\n", " Class: 1 Class: 2 Class: 3 Class: 4\n", "Sensitivity 0.3750 0.6250 0.8690 NA\n", "Specificity 0.9080 0.8185 0.9240 0.856\n", "Pos Pred Value 0.6708 0.6326 0.8511 NA\n", "Neg Pred Value 0.7440 0.8136 0.9338 NA\n", "Prevalence 0.3333 0.3333 0.3333 0.000\n", "Detection Rate 0.1250 0.2083 0.2897 0.000\n", "Detection Prevalence 0.1863 0.3293 0.3403 0.144\n", "Balanced Accuracy 0.6415 0.7218 0.8965 NA" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "caret::confusionMatrix(factor(clusters), factor(Z, levels=c(levels(Z), 4)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously, the assignment suffers from the fact that the Poisson components are not very well separated. However, the clustering is still fairly good." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## License\n", "\n", "
\n", "\n", "The case study is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License." ] } ], "metadata": { "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.0.0" } }, "nbformat": 4, "nbformat_minor": 2 }